Why are there so many inactive processes running on my computer?, etc.

It is normal for there to be quite a number of inactive processes.

the inactive processes take up half of the system memory

There is some confusion in what you are asking. Are you talking about inactive memory? Inactive processes will not be using any CPU, but they may have inactive memory allotted to them. This is memory that, should another process require it, can be reallocated to that other process. It's like a kind of caching: it can quickly be drawn upon should the inactive process become active again and need it. In the meantime, it is free for any process to use. It is not being wasted or used.

Usually, how much space is this supposed to take?

You are introducing the word "space" here. I'm not sure what you mean by that, but I don't think it's applicable.

I've been trying to check to see what's running but sometimes some disappear and appear momentarily.

That is normal for Activity Monitor. I think you need to have a better understanding of Activity Monitor.

http://oreilly.com/pub/a/mac/2005/10/04/activity-monitor.html

Sophos may be slowing down your computer. You should turn off its always-on scanning feature (or whatever it's called) and just run it on demand.

Hi Melancholy --

. . . my MacBook Pro has been really slow lately.

In relation to "lately," what things have you changed or added just before the lately?
Does this always or usually happen in Safari, or on your computer, overall?
Sophos will slow you down quite a bit, IMHO.